Question 13 Marks
Which of the two rational numbers is greater in the following pairs? $\frac{9}{-13}\text{ or }\frac{7}{-12}$
Answer$\frac{9}{-13}\text{ or }\frac{7}{-12}$
$\Rightarrow\frac{9\times(-1)}{-13\times(-1)}\text{ or }\frac{7\times(-1)}{-12\times(-1)}$
$\Rightarrow\frac{-9}{13}\text{ or }\frac{-7}{12}$ (Making denominator positive)
$LCM$ of $13$ and $12 = 156$
$\therefore\frac{-9}{13}=\frac{-9\times12}{13\times12}=\frac{-108}{156}$
$\frac{-7}{12}=\frac{-7\times13}{12\times13}=\frac{-91}{156}$
It is clear that $\frac{-91}{156}\text{ or }\frac{-7}{12}\text{ or }\frac{7}{-12}$ is greater.
View full question & answer→Question 23 Marks
Evaluate: $\frac{-5}{-8}-\frac{-3}{4}$
Answer$\frac{-5}{-8}-\frac{-3}{4}$
$\frac{-5}{-8}=\frac{-5\times(-1)}{-8\times(-1)}=\frac{5}{8}$
$LCM$ of $8$ and $4 = 8$
$\therefore\frac{-3}{4}=\frac{-3\times2}{4\times2}=\frac{-6}{8}$
$\therefore\frac{-5}{-8}-\frac{-3}{4}$
$=\frac{5}{8}-\Big(\frac{-6}{8}\Big)$
$=\frac{5}{8}+\frac{6}{8}$
$=\frac{5+6}{8}$
$=\frac{11}{8}$
View full question & answer→Question 33 Marks
What should be added to $\Big(\frac{-13}{4}+\frac{-3}{8}\Big)$
Answer$1-\Big(\frac{-13}{4}+\frac{-3}{8}\Big)$
$LCM$ of $4$ and $8 = 8$
$\therefore1=\frac{1\times8}{1\times8}=\frac{8}{8}$
$\frac{-13}{4}=\frac{-13\times2}{4\times2}=\frac{-26}{8}$
$\therefore1-\Big(\frac{-13}{4}+\frac{-3}{8}\Big)$
$=\frac{8}{8}-\Big(\frac{-26}{8}+\frac{-3}{8}\Big)$
$=\frac{8}{8}+\frac{26}{8}+\frac{3}{8}$
$=\frac{8+26+3}{8}=\frac{37}{8}$
View full question & answer→Question 43 Marks
By what number should $\frac{-44}{9}$ be divided to get $\frac{-11}{3}?$
AnswerLet the required number be x$\frac{-44}{9}\div\text{x}=\frac{-11}{3}$
$\Rightarrow\text{x}=\frac{44}{9}\times\frac{3}{-11}$
$\Rightarrow\text{x}=\frac{4}{3}$
View full question & answer→Question 53 Marks
Find five rational numbers between $-3$ and $-2.$
Answer5 rational numbers between $-3$ and $-2$
We can write $-3=\frac{-3\times6}{6}=\frac{-18}{6}$
$\Rightarrow-2=\frac{-2\times6}{6}=\frac{-12}{6}$
$\Rightarrow-2=\frac{-2\times6}{6}=\frac{-12}{6}$
$\Rightarrow\frac{-18}{6}<\frac{-12}{6}$
$\Rightarrow\frac{-18}{6}<\frac{-17}{6}<\frac{-16}{6}<\frac{-15}{6}$
$<\frac{-14}{6}<\frac{-13}{6}<\frac{-12}{6}$
$\therefore$ Five rational number between $-3$ and $-2$ will be $\frac{-17}{6},\frac{16}{6},\frac{-15}{6},\frac{-14}{6}\frac{-13}{6}$
View full question & answer→Question 63 Marks
Add the following rational numbers: $\frac{-9}{24}\text{and}\frac{-1}{18}$
Answer$\frac{-9}{24}\text{and}\frac{-1}{18}$
$LCM$ of $24$ and $18 = 72$
$\therefore\frac{-9}{24}=\frac{-9\times3}{24\times3}=\frac{-27}{72}$
$\frac{-1}{18}=\frac{-1\times4}{18\times4}=\frac{-4}{72}$
$\therefore\frac{-9}{24}+\frac{-1}{18}=\frac{-27}{72}+\frac{-4}{72}$
$=\frac{-27+(-4)}{72}=\frac{-27-4}{72}$
$=\frac{-31}{72}$
View full question & answer→Question 73 Marks
Subtract:
$\frac{-5}{6}\text{ from }\frac{1}{3}$
Answer$\frac{-5}{6}\text{ from }\frac{1}{3}$
$Lcm$ of $6$ and $3 = 6$
$\therefore\frac{1}{3}=\frac{1\times2}{3\times2}=\frac{2}{6}$
$\therefore\frac{1}{3}-\Big(\frac{-5}{6}\Big)=\frac{1}{3}+\frac{5}{6}$
$=\frac{2}{6}+\frac{5}{6}=\frac{2+5}{6}=\frac{7}{6}$
View full question & answer→Question 83 Marks
The sum of two rational numbers is $\frac{-3}{8}$ If one of them is $\frac{3}{16}$ find the other.
AnswerSum of two numbers $=\frac{-3}{8}$
One number $=\frac{3}{16}$
$\therefore$ second number $=\frac{-3}{8}-\frac{3}{16}$
$(LCM$ of $8$ and $16 = 16)$
$=\frac{-6-3}{16}=\frac{-9}{16}$
View full question & answer→Question 93 Marks
Add the following rational numbers: $-4\text{ and }\frac{1}{2}$
Answer$-4\text{ and }\frac{1}{2}$
$\frac{-4}{1}=\frac{-4\times2}{1\times2}=\frac{-8}{2}$
$\therefore \ -4+\frac{1}{2}=\frac{-8}{2}+\frac{1}{2}$
$=\frac{-8+1}{2}=\frac{-7}{2}$
View full question & answer→Question 103 Marks
A bus is moving at an average speed of $46\frac{2}{3}\text{km/h}$ How much distance will it cover in $2\frac{2}{5}\text{hours?}$
AnswerSpeed of bus $46\frac{2}{3}\text{km/h}$
$\frac{140}{3}\text{km/h}$
Distance covered in $2\frac{2}{5}\text{hours}$
$=\frac{140}{3}\times2\frac{2}{5}\text{km}$
$=\frac{140}{3}\times\frac{12}{5}\text{km}=112\text{km}.$
View full question & answer→Question 113 Marks
The sum of two rational numbers is $\frac{4}{21}$ If one of them is $\frac{5}{7}$ find the other.
AnswerSum of two numbers $=\frac{4}{21}$
One number $=\frac{5}{7}$
$\therefore$ second number $=\frac{4}{21}-\frac{5}{7}$
$(LCM$ of $21$ and $7 = 21)$
$=\frac{4-15}{21}=\frac{-11}{21}$
View full question & answer→Question 123 Marks
Simplify: $2+\frac{-1}{2}+\frac{-3}{4}$
Answer$2+\frac{-1}{2}+\frac{-3}{4}$
$LCM$ of $2, 4 = 4$
$\therefore\frac{2}{1}=\frac{2\times4}{1\times4}=\frac{8}{4}$
$\frac{-1}{2}=\frac{-1\times2}{2\times2}=\frac{-2}{4}$
$\frac{-3}{4}=\frac{-3}{4}$
$\therefore \ 2+\frac{-1}{2}+\frac{-3}{4}$
$=\frac{8}{4}+\frac{-2}{4}+\frac{-3}{4}$
$=\frac{8+(-2)+(-3)}{4}$
$=\frac{8-2-3}{4}=\frac{8-5}{4}$
$=\frac{3}{4}$
View full question & answer→Question 133 Marks
Simplify:
$\Big(\frac{16}{15}\times\frac{-25}{8}\Big)+\Big(\frac{-14}{27}\times\frac{6}{7}\Big)$
Answer$\Big(\frac{16}{15}\times\frac{-25}{8}\Big)+\Big(\frac{-14}{27}\times\frac{6}{7}\Big)$
$=\frac{16\times(-25)}{15\times8}+\frac{-14\times6}{27\times7}$
$=\frac{2\times(-5)}{1\times1}+\frac{-2\times2}{9\times1}$
$=\frac{-10}{3}+\frac{-4}{9}=\frac{-30+(-4)}{9}$
$=\frac{-30-4}{9}$
$(LCM$ of $3, 9 = 9)$
$=\frac{-34}{9}$
View full question & answer→Question 143 Marks
Simplify: $\frac{16}{-21}\times\frac{-14}{5}$
Answer$\frac{16}{-21}\times\frac{-14}{5}$$\frac{16}{-21}=\frac{16\times(-1)}{-21\times(-1)}$
$=\frac{-16}{21}$
$\therefore\frac{-16}{21}\times\frac{14}{5}$
$=\frac{(-16)\times(-14)}{21\times5}$
$=\frac{(-16)\times(-2)}{3\times5}$
$=\frac{32}{15}$
View full question & answer→Question 153 Marks
Evaluate: $\frac{4}{9}-\frac{2}{-3}$
Answer$\frac{4}{9}-\frac{2}{-3}$ $LCM$ of $9$ and $3 = 9$
$\therefore\frac{2}{-3}=\frac{2\times(-1)}{-3\times(-1)}=\frac{-2}{3}$
$=\frac{-2\times3}{3\times3}=\frac{-6}{9}$
$\therefore\frac{4}{9}-\frac{2}{-3}=\frac{4}{9}-\Big(\frac{-6}{9}\Big)$
$=\frac{4}{9}+\frac{6}{9}$ $=\frac{4+6}{9}$
$=\frac{10}{9}$
View full question & answer→Question 163 Marks
Subtract:
$5\text{ from }\frac{-3}{5}$
Answer $5\text{ from }\frac{-3}{5}$
$\frac{5}{1}=\frac{5\times5}{1\times5}=\frac{25}{5}$
$\therefore\frac{-3}{5}-\frac{5}{1}=\frac{-3}{5}-\frac{25}{5}$
$=\frac{-3-25}{5}=\frac{-28}{5}$
View full question & answer→Question 173 Marks
Simplify: $\frac{-8}{15}+\frac{2}{3}$
Answer$\frac{-8}{15}+\frac{2}{3}$
$=\frac{-8}{15}+\frac{2\times(-1)}{-3\times(-1)}$
$=\frac{-8}{15}+\frac{-2}{3}$
$LCM$ of $15, 3 = 15$
$\frac{-2}{3}=\frac{-2\times5}{3\times5}=\frac{-10}{15}$
$\therefore \ \frac{-8}{15}+\frac{-2}{3}=\frac{-8}{15}+\frac{-10}{15}$
$=\frac{-8+(-10)}{15}=\frac{-8-10}{15}$
$=\frac{-18}{15}=\frac{-18\div3}{15\div3}=\frac{-6}{5}$
View full question & answer→Question 183 Marks
Subtract: $\frac{-13}{9}\text{ from }0$
Answer$\frac{-9}{7}\text{ from }-1$$0-\Big(\frac{-13}{9}\Big)=0+\frac{13}{9}$
$=\frac{13}{9}$
View full question & answer→Question 193 Marks
Simplify: $\Big(\frac{13}{8}\times\frac{12}{13}\Big)+\Big(\frac{-4}{9}\times\frac{3}{-2}\Big)$
Answer$\Big(\frac{13}{8}\times\frac{12}{13}\Big)+\Big(\frac{-4}{9}\times\frac{3}{-2}\Big)$
$\Big\{\frac{3}{-2}=\frac{3\times(-1)}{-2\times(-1)}=\frac{-3}{2}\Big\}$
$\Big(\frac{13}{8}\times\frac{12}{13}\Big)+\Big(\frac{-4}{9}\times\frac{-3}{2}\Big)$
$=\frac{13\times12}{8\times12}+\frac{(-4)\times(-3)}{9\times2}$
$=\frac{3}{2}+\frac{(-2)+(-1)}{3\times1}=\frac{3}{2}+\frac{2}{3}$ $(LCM$ of $2$ and $3 = 6)$ $=\frac{9+4}{6}=\frac{13}{6}$
View full question & answer→Question 203 Marks
Subtract: $\frac{5}{9}\text{ from }\frac{-2}{3}$
Answer$\frac{5}{9}\text{ from }\frac{-2}{3}$$LCM$ of $9$ and $3 = 9$
$\therefore\frac{-2}{3}=\frac{-2\times3}{3\times3}=\frac{-6}{9}$
$\frac{-2}{5}-\frac{5}{9}=\frac{-6}{9}-\frac{5}{9}$
$=\frac{-6-5}{9}=\frac{-11}{9}$
View full question & answer→Question 213 Marks
Multiply: $\frac{25}{-9}\text{ by }\frac{3}{-10}$
Answer$\frac{25}{-9}\text{ by }\frac{3}{-10}$
$=\frac{25}{-9}\times\frac{3}{-10}=\frac{25}{-9}$
$=\frac{25\times(-1)}{-9\times(-1)}=\frac{-25}{9}$
$\frac{3}{-10}=\frac{3\times(-1)}{-10\times(-1)}$
$=\frac{-3}{10}=\frac{3\times(-1)}{-10\times(-1)}$
$=\frac{-3}{10}=\frac{(-25)\times(-3)}{9\times10}$
$=\frac{(-5)\times(-1)}{3\times2}=\frac{5}{6}$
View full question & answer→Question 223 Marks
Simplify: $\Big(\frac{6}{55}\times\frac{-22}{9}\Big)+\Big(\frac{-26}{125}\times\frac{-10}{39}\Big)$
Answer$\Big(\frac{6}{55}\times\frac{-22}{9}\Big)+\Big(\frac{-26}{125}\times\frac{-10}{39}\Big)$
$=\frac{6\times(-22)}{55\times9}+\frac{-26\times(-10)}{125\times39}$
$=\frac{2\times(-2)}{5\times3}+\frac{2\times(-2)}{25\times3}$
$=\frac{-4}{15}-\frac{-4}{75}=\frac{-4}{15}+\frac{4}{75}$ $(LCM$ of $15$ and $75 = 75)$
$=\frac{-20+4}{75}$$=\frac{-16}{75}$
View full question & answer→Question 233 Marks
Evaluate: $\frac{3}{4}-\frac{4}{5}$
Answer$\frac{3}{4}-\frac{4}{5}$
$LCM$ of $4$ and $5 = 20$
$\frac{3}{4}=\frac{3\times5}{4\times5}=\frac{15}{20}$
$\frac{4}{5}=\frac{4\times4}{5\times4}=\frac{16}{20}$
$\therefore\frac{3}{4}-\frac{4}{5}$
$=\frac{15}{20}-\frac{16}{20}$
$=\frac{15-16}{20}$$=\frac{-1}{20}$
View full question & answer→Question 243 Marks
Which of the two rational numbers is greater in the following pairs? $\frac{5}{9}\text{ or }\frac{-3}{-8}$
Answer$\frac{5}{9}\text{ or }\frac{-3}{-8}$
$\Rightarrow\frac{5}{9}\text{ or }\frac{-3\times(-1)}{-8\times(-1)}$
$\Rightarrow\frac{5}{9}\text{ or }\frac{3}{8}$ (Making denominator positive)
$LCM$ of $9$ and $8 = 72$
$\therefore\frac{5}{9}=\frac{5\times8}{9\times8}=\frac{40}{72}$
$\frac{3}{8}=\frac{3\times9}{8\times9}=\frac{27}{72}$
It is clear that $40 > 27$
$\therefore\frac{40}{72}\text{ or }\frac{5}{9}\text{ is greater}.$
View full question & answer→Question 253 Marks
What should be added to $\frac{-7}{8}$ to get $\frac{5}{9}?$
AnswerLet the required number be $x$ $\text{x}+\Big(\frac{-7}{8}\Big)$
$\Rightarrow\text{x}=\frac{5}{9}-\Big(\frac{-7}{8}\Big)$
$=\frac{5}{9}+\frac{-7}{8}$
$LCM$ of $9$ and $8$ is $72$ $=\frac{40+63}{72}$
$\frac{103}{72}$
Hence, the other number is $\frac{103}{72}$
View full question & answer→Question 263 Marks
Which of the two rational numbers is greater in the following pairs? $\frac{4}{-3}\text{ or }\frac{-8}{7}$
Answer$\frac{4}{-3}\text{ or }\frac{-8}{7}$
$\Rightarrow\frac{4\times(-1)}{-3\times(-1)}\text{ or }\frac{-8}{7}$
$\Rightarrow\frac{-4}{3}\text{ or }\frac{-8}{7}$ $LCM$ of $3$ and $7 = 21$
$\therefore\frac{-4}{3}=\frac{-4\times7}{3\times7}=\frac{-28}{21}$
$\frac{-8}{7}=\frac{-8\times3}{7\times3}=\frac{-24}{21}$
It is clear that $\frac{-24}{21}\text{ or }\frac{-8}{7}$ is greater.
View full question & answer→Question 273 Marks
Evaluate: $\frac{7}{11}-\frac{-4}{-11}$
Answer$\frac{7}{11}-\frac{-4}{-11}$
$\frac{-4}{-11}=\frac{-4\times(-1)}{-11\times(-1)}=\frac{4}{11}$
$\therefore\frac{7}{11}-\frac{4}{11}$
$=\frac{7-4}{11}$
$=\frac{3}{11}$
View full question & answer→Question 283 Marks
Evaluate: $\frac{7}{24}-\frac{19}{36}$
Answer$\frac{7}{24}-\frac{19}{36}$
$LCM$ of $24$ and $36 = 72$
$\therefore\frac{7}{24}=\frac{7\times3}{24\times3}=\frac{21}{72}$
$\frac{19}{36}=\frac{19\times2}{36\times2}=\frac{38}{72}$
$\therefore\frac{7}{24}-\frac{19}{36}$
$=\frac{21}{72}-\frac{38}{72}$
$=\frac{21-38}{72}$
$=\frac{-17}{72}$
View full question & answer→Question 293 Marks
By what rational number should $\frac{-8}{39}$ be multiplied to obtain $\frac{5}{26}?$
Answer Product of two numbers $=\frac{5}{26}$
One number $=\frac{-8}{39}$
$\therefore$ Second number $\frac{5}{26}\div\Big(\frac{-8}{39}\Big)$
$=\frac{5}{26}\times\frac{39}{8}$
$=\frac{5\times3}{2\times(-8)}$
$=\frac{15\times(-1)}{(-16)\times(-1)}$
$=\frac{-15}{16}$
View full question & answer→Question 303 Marks
Subtract:
$\frac{-32}{13}\text{ from }\frac{-6}{5}$
Answer$\frac{-32}{13}\text{ from }\frac{-6}{5}$
$LCM$ of $13$ and $5 = 65$
$\frac{-6}{5}=\frac{-6\times13}{5\times13}=\frac{-78}{65}$
$\frac{-32}{13}=\frac{-32\times5}{13\times5}=\frac{-160}{65}$
$\therefore\frac{-6}{5}-\Big(\frac{-32}{13}\Big)=\frac{-6}{5}+\frac{32}{13}$
$=\frac{-78}{65}+\frac{160}{65}=\frac{-78+160}{65}$
$=\frac{82}{65}$
View full question & answer→Question 313 Marks
Express the following rational numbers in standard form: $\frac{-46}{115}$
Answer$\frac{-46}{115}$ $H.C.F.$ of $46$ and $115$ is $23$ Dividing both the numerator and the denominator by $23$ $=\frac{-46\div23}{115\div23}$ $=\frac{-2}{5}$
View full question & answer→Question 323 Marks
Evaluate: $-3-\frac{4}{7}$
Answer$-3-\frac{4}{7}$ $=\frac{-3}{1}-\frac{4}{7}$ $LCM$ of $1$ and $7 = 7$
$\therefore\frac{-3}{1}=\frac{-3\times7}{1\times7}=\frac{-21}{7}$
$\therefore\frac{-21}{7}-\frac{4}{7}$
$=\frac{-21-4}{7}$ $=\frac{-25}{7}$
View full question & answer→Question 333 Marks
Add the following rational numbers: $\frac{27}{-4}\text{ and }\frac{-15}{8}$
Answer$\frac{27}{-4}\text{ and }\frac{-15}{8}$
$\frac{27}{-4}=\frac{27\times(-1)}{-4\times(-1)}=\frac{-27}{4}$
$\Rightarrow\frac{-27}{4}\times\frac{2}{2}=\frac{-54}{8}$
$\therefore \frac{-27}{4}+\frac{-15}{8}=\frac{-54}{8}+\frac{-15}{8}$
$=\frac{-54+(-15)}{8}$
$=\frac{-54-15}{8}=\frac{-69}{8}$
View full question & answer→Question 343 Marks
How many pieces, each of length $3\frac{3}{4}\text{m}$ can be cut from a rope of length $30$ metres?
AnswerTotal length of rape $= 30m$ Lenghth of one piece $=3\frac{3}{4}$
$=\frac{15}{4}\text{m}$
$\therefore$ No. of pieces of rope $=30\div\frac{15}{4}$
$=30\times\frac{4}{15}=2\times4$
$=8\text{ pieces}$
View full question & answer→Question 353 Marks
Express the following rational numbers in standard form: $\frac{-209}{247}$
Answer$\frac{-209}{247}$ $H.C.F.$ of $209$ and $247$ is $19$
Dividing both the numerator and the denominator by $19$ $=\frac{-209\div19}{247\div19}$ $=\frac{-11}{13}$
View full question & answer→Question 363 Marks
List five rational numbers between $-2$ and $-1.$
Answer$-2=\frac{-2\times6}{1\times6}=\frac{12}{6}$
$-1=\frac{-1\times6}{1\times6}=\frac{-6}{6}$
The interger between $-12$ and $-6$ are $-11, -10, -9, -8, -7$
Hence, fiver rational numbers between $-2$ and $-1$ are $\frac{-11}{6},\frac{10}{6},\frac{-9}{6},\frac{-8}{6},\frac{-7}{6}$
View full question & answer→Question 373 Marks
Subtract: $\frac{3}{4}\text{ from }\frac{1}{3}$
Answer$\frac{3}{4}\text{ from }\frac{1}{3}$ $Lcm$ of $4$ and $3 = 12$
$\therefore\frac{3}{4}=\frac{3\times3}{4\times3}=\frac{9}{12}$
$\frac{1}{3}=\frac{1\times4}{3\times4}=\frac{4}{12}$
$\therefore\frac{1}{3}-\frac{3}{4}=\frac{4}{12}-\frac{9}{12}$
$=\frac{4-9}{12}=\frac{-5}{12}$
View full question & answer→Question 383 Marks
Subtract: $\frac{-8}{9}\text{ from }\frac{-3}{5}$
Answer$\frac{-8}{9}\text{ from }\frac{-3}{5}$$Lcm$ of $9$ and $5 = 45$
$\therefore\frac{-8}{9}=\frac{-8\times5}{9\times5}=\frac{-40}{45}$
$\frac{-3}{5}=\frac{-3\times9}{5\times9}=\frac{-27}{45}$
$\therefore\frac{-3}{5}-\Big(\frac{-8}{9}\Big)=\frac{-3}{5}+\frac{8}{9}$
$=\frac{27}{45}+\frac{-27+40}{45}=\frac{13}{45}$
View full question & answer→Question 393 Marks
Find the cost of $3\frac{1}{3}\text{metre}$ metres of cloth at $\text{Rs. }40\frac{1}{2}\text{\metre.}$
AnswerCost of $1$ metre of cloth $=\text{Rs. }40\frac{1}{2}$
$=\text{Rs. }\frac{81}{2}$
$\therefore\text{ cost of }3\frac{1}{3}\text{m}\text{ cloth }$
$=\text{Rs. }\frac{81}{2}\times3\frac{1}{3}$
$=\text{Rs. }\frac{81}{2}\times\frac{10}{3}$
$=\text{Rs. }135$
View full question & answer→Question 403 Marks
A car is moving at an average speed of $56\frac{3}{5}\text{km/h}$ How much distance will it cover in $7\frac{1}{2}$ hours?
AnswerAverage speed $=56\frac{3}{5}\text{km/h}$
$=\frac{283}{5}\text{km/h}$ Time $=7\frac{1}{2}\text{h}=\frac{15}{2}\text{h}$
Distance = Speed $\times$ time $=\frac{283}{5}\times\frac{1.5}{2}$
$=424\frac{1}{2}\text{km}$
The car will cover $424\frac{1}{2}\text{km in }7\frac{1}{2}\text{h}$
View full question & answer→Question 413 Marks
Find five rational numbers between $\frac{-3}{5}\text{ and }\frac{-1}{2}$
Answer$LCM$ of $5$ and $2 = 10$
Now $\frac{-3}{5}=\frac{-3\times2}{5\times2}=\frac{-6}{10}$
$=\frac{-6\times6}{10\times6}=\frac{-36}{60}$
and $\frac{-1}{2}=\frac{-1\times5}{2\times5}=\frac{-5}{10}$
$=\frac{-5\times6}{10\times6}=\frac{-30}{60}$
and $\frac{-36}{60}<\frac{-35}{60}<\frac{-34}{60}<\frac{-33}{60}$
$<\frac{-32}{60}<\frac{-31}{60}<\frac{-30}{60}$
$\therefore$ five rational numbers between $\frac{-3}{5}$ and $\frac{-1}{2}$ are $\frac{-36}{60}<\frac{-34}{60}<\frac{-33}{60}<\frac{-32}{60}<\frac{-31}{60}$
View full question & answer→Question 423 Marks
Subtract: $\frac{-9}{7}\text{ from }-1$
Answer$\frac{-9}{7}\text{ from }-1$$\frac{-1}{1}=\frac{-1\times7}{1\times7}=\frac{-7}{7}$
$\therefore-1-\Big(\frac{-9}{7}\Big)=-1+\frac{9}{7}$
$=\frac{-7}{7}+\frac{9}{7}=\frac{-7+9}{7}=\frac{2}{7}$
View full question & answer→Question 433 Marks
Multiply: $\frac{-36}{5}\text{ by }\frac{20}{-3}$
Answer$\frac{-36}{5}\text{ by }\frac{20}{-3}$
$=\frac{20}{-3}=\frac{20\times(-1)}{-3\times(-1)}$
$=\frac{-20}{3}=\frac{20\times(-1)}{-3\times(-1)}$
$=\frac{-20}{3}$
$\therefore\frac{-36}{5}\times\frac{-20}{3}$
$=\frac{-36}{5}\times\frac{-20}{3}$
$=\frac{(-36)\times(-20)}{5\times3}$
$=\frac{(-12)\times(-4)}{1\times1}=\frac{48}{1}=48$
View full question & answer→Question 443 Marks
Simplify: $\frac{5}{-18}\times\frac{-9}{20}$
Answer$\frac{5}{-18}\times\frac{-9}{20}$
$\frac{5}{-18}=\frac{5\times(-1)}{-18\times(-1)}$
$=\frac{-5}{18}$
$\therefore\frac{-5}{18}\times\frac{-9}{20}$
$=\frac{(5)\times(-9)}{18\times20}$
$=\frac{(-1)\times(-1)}{2\times4}$
$=\frac{1}{8}$
View full question & answer→Question 453 Marks
Add the following rational numbers: $\frac{-2}{5}\text{ and }\frac{3}{4}$
Answer$\frac{-2}{5}\text{ and }\frac{3}{4}$
$\frac{-2}{5}=\frac{-2\times4}{5\times4}=\frac{-8}{20}$
$\frac{3}{4}=\frac{3\times5}{4\times5}=\frac{15}{20}$
$\therefore \ \frac{-2}{5}+\frac{3}{4}=\frac{-8}{20}+\frac{15}{20}$
$=\frac{-8+15}{20}=\frac{7}{20}$
View full question & answer→Question 463 Marks
Simplify: $\Big(\frac{-12}{7}\times\frac{-14}{27}\Big)+\Big(\frac{-8}{45}\times\frac{9}{16}\Big)$
Answer$\Big(\frac{-12}{7}\times\frac{-14}{27}\Big)+\Big(\frac{-8}{45}\times\frac{9}{16}\Big)$
$=\frac{(-12)\times(-14)}{7\times27}+\frac{-8\times9}{45\times16}$
$=\frac{-4\times(-2)}{1\times9}+\frac{-1\times1}{5\times2}$
$=\frac{8}{9}-\frac{-1}{10}=\frac{8}{9}+\frac{1}{10}$ $(LCM$ of $9$ and $10 = 90)$ $=\frac{80+9}{90}$
$=\frac{89}{90}$
View full question & answer→Question 473 Marks
Add the following rational numbers: $\frac{-5}{36}\text{ and }\frac{-7}{12}$
Answer$\frac{-5}{36}\text{ and }\frac{-7}{12}$
$=\frac{-7}{12}=\frac{-7\times3}{12\times3}=\frac{-21}{36}$
$( \because\text{LCM }\text{of }36,12=36)$
$\therefore\frac{-5}{36}+\frac{-5}{36}=\frac{-5}{36}+\frac{-21}{36}$
$=\frac{-5+(-21)}{36}=\frac{-5-21}{36}$
$=\frac{-26}{36}$ $($Dividing by $2)$ $=\frac{-13}{18}$
View full question & answer→Question 483 Marks
Subtract: $-7\text{ from }\frac{-4}{7}$
Answer$-7\text{ from }\frac{-4}{7}$
$\frac{-7}{1}=\frac{-7\times7}{1\times7}=\frac{-49}{7}$
$\therefore\frac{-4}{7}-\Big(\frac{-7}{1}\Big)=\frac{-4}{7}+\frac{7}{1}$
$=\frac{-4}{7}+\frac{49}{7}=\frac{-4+49}{7}$
$=\frac{45}{7}$
View full question & answer→Question 493 Marks
The product of two rational numbers is $\frac{-16}{2}.$ If one of the numbers is $\frac{-4}{3},$ find the other.
AnswerProduct of two numbers $=\frac{-16}{9}$ One number $=\frac{-16}{9}$
$\therefore$ Second number $\Big(\frac{-16}{9}\Big)\div\Big(\frac{-4}{3}\Big)$
$=\frac{-16}{9}\times\frac{3}{-4}$
$=\frac{-16\times3}{9\times(-4)}$
$=\frac{-4\times1}{3\times(-1)}$
$=\frac{-4}{-3}=\frac{4}{3}$
View full question & answer→Question 503 Marks
The sum of two rational numbers is $\frac{-4}{3}$ If one of them is $-5$ find the other.
AnswerSum of two numbers $=\frac{-4}{3}$
One number $-5$
$\therefore$ second number $=\frac{-4}{3}-(-5)$
$=\frac{-4}{3}+\frac{5}{1}$
$=\frac{-4+15}{3}=\frac{11}{3}$
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